% This file: (find-LATEX "2019J-ops-defs.tex")
%  Based on: (find-LATEX "2017planar-has-defs.tex")
%
% «.defs»		(to "defs")
% «.squigbij»		(to "squigbij")
% «.chars»		(to "chars")

%  ____        __     
% |  _ \  ___ / _|___ 
% | | | |/ _ \ |_/ __|
% | |_| |  __/  _\__ \
% |____/ \___|_| |___/
%                     
% «defs»  (to ".defs")

% Equivalence relations:
%\def\eqP{\underset{P}{\sim}}
%\def\eqJ{\underset{J}{\sim}}
%\def\eqP{\underset{\scriptscriptstyle P}{\sim}}
%\def\eqJ{\underset{\scriptscriptstyle J}{\sim}}
\def\eqN{\sim_1}
\def\eqP{\sim_P}
\def\eqJ{\sim_J}
\def\eqL{\sim_L}
\def\eqR{\sim_R}
\def\eqS{\sim_S}
\def\eqF{\sim_F}
\def\eqQ{\sim_Q}
\def\eqQp{\sim_{Q'}}

\def\BPM{\mathsf{BPM}}
\def\WPM{\mathsf{WPM}}
\def\ZHAG{\mathsf{ZHAG}}

\def\LR{\mathbb{LR}}

\def\catTwo{\mathbf{2}}
\def\calS{\mathcal{S}}
\def\calI{\mathcal{I}}
\def\calK{\mathcal{K}}
\def\calV{\mathcal{V}}

\def\und#1#2{\underbrace{#1}_{#2}}

\def\ECa {\mathsf{EC}{∧}}

\def\ECube{\mathsf{ECube}}   \def\ecube{\mathsf{ecube}}
\def\OCube{\mathsf{OCube}}   \def\ocube{\mathsf{ocube}}
\def\FCube{\mathsf{FCube}}   \def\fcube{\mathsf{fcube}}
\def\SCube{\mathsf{SCube}}   \def\fcube{\mathsf{fcube}}
\def\VCube{\mathsf{VCube}}   \def\vcube{\mathsf{vcube}}
\def\Exprs{\mathsf{Exprs}}
\def\Thms {\mathsf{Thms}}
\def\thms {\mathsf{thms}}
\def\vthms{\mathsf{vthms}}
\def\NClasses{\mathsf{NClasses}}
\def\nclasses{\mathsf{nclasses}}
\def\ZHAstar{ZHA${}^*$}
\def\sfE{\mathsf{E}}
\def\sfV{\mathsf{V}}

\def\oand{\varowedge}
\def\oor {\varovee}
\def\oimp{\mathbin{\buildoimp{\ominus}{\to}}}
\def\buildoimp#1#2{\rlap{$#1$}\hbox{$#2$}}

\def\zs{{0\ldots7}}

\def\pile            {\mathsf{pile}}
\def\pileelements#1#2{{\{#1▁, \ldots, 1▁, \; ▁1, \ldots, ▁#2\}}}

% Derivation rules.
%
% From: (p2ap 10 "2._J-operators")
%       (p2aa    "2._J-operators")
\def\J   {\mathsf{J}}
\def\MP  {\mathsf{MP}}
\def\Mo  {\mathsf{Mo}}
\def\Mop {\mathsf{Mop}}
\def\Sand{\mathsf{Sand}}
\def\ECa {\mathsf{EC}{\&}}
\def\ECv {\mathsf{EC}{∨}}
\def\ECS {\mathsf{ECS}}
%
% From: (p2ap 12 "3._midway")
%       (p2aa    "3._midway")
\def\NoLcuts{\mathsf{No}λ\mathsf{cuts}}
\def\NoYcuts{\mathsf{NoYcuts}}
\def\astarcube{{\&}^*\mathsf{Cube}}
\def\ostarcube{{∨}^*\mathsf{Cube}}
\def\istarcube{{→}^*\mathsf{Cube}}
\def\acz{{\&}^*\mathsf{C}_0}
\def\ocz{{∨}^*\mathsf{C}_0}
\def\icz{{→}^*\mathsf{C}_0}
%
\def\astarcuben{{\&}^*\mathsf{Cube}_\mathsf{n}}
\def\ostarcuben{{∨}^*\mathsf{Cube}_\mathsf{n}}
\def\istarcuben{{→}^*\mathsf{Cube}_\mathsf{n}}
\def\astarcubev{{\&}^*\mathsf{Cube}_\mathsf{v}}
\def\ostarcubev{{∨}^*\mathsf{Cube}_\mathsf{v}}
\def\istarcubev{{→}^*\mathsf{Cube}_\mathsf{v}}


\def\ltor#1#2{#1\_{\to}\_#2}
\def\lotr#1#2{#1\_{\ot}\_#2}
\def\Int{{\operatorname{int}}}
\def\Int{{\operatorname{\mathsf{int}}}}
\def\coInt{{\operatorname{\mathsf{coint}}}}
%\def\Opens{{\mathcal{O}}}
%
\def\LC {\mathsf{LC}}
\def\RC {\mathsf{RC}}
\def\TCG{\mathsf{2CG}}
\def\pile{\mathsf{pile}}
\def\ltor#1#2{#1\_{\to}\_#2}
\def\lotr#1#2{#1\_{\ot}\_#2}
\def\ltol#1#2{#1\_{\to}#2\_}
\def\rtor#1#2{\_#1{\to}\_#2}
%
%
%\catcode`∧=13 \def∧{\mathop{\&}}

\def\biggest {\mathsf{biggest}}
\def\smallest{\mathsf{smallest}}
\def\Cuts    {\mathsf{Cuts}}

\def\myresizebox#1{%
  \noindent\hbox to \textwidth{\hss
    \resizebox{1.0\textwidth}{!}{#1}%
    \hss}
  }





%                  _  _ _     _  _ 
%  ___  __ _ _   _(_)(_) |__ (_)(_)
% / __|/ _` | | | | || | '_ \| || |
% \__ \ (_| | |_| | || | |_) | || |
% |___/\__, |\__,_|_|/ |_.__/|_|/ |
%         |_|      |__/       |__/ 
%
% «squigbij»  (to ".squigbij")
% From: (find-LATEX "2017planar-has-defs.tex" "squigbij")
%
\def\squigbij{\newsquigbij}
%\def\oldsquigbij{\;\; \diagxyto/<~>/<300> \;\;}
\def\newsquigbij{\;\; \squigbijbody \;\;}
\def\squigbijy{-1.2}
\def\squigbijbody{\squigbijbodywithparams{1.5pt}{0.3pt}{1.0}}
\def\squigbijtriangle(#1,#2)#3{\polygon*(#1,0)(#2,#3)(#2,-#3)}
\def\squigbijbodywithparams#1#2#3{{%
  \unitlength=#1
  \linethickness{#2}
  % \beginpicture(-5,-1)(17,1)%
  % \begin{picture}(22.4,2.4)(-5.2,-1.2)%
  \begin{picture}(22.4,2.4)(-5.2,\squigbijy)%
    \polyline(-3,0)(0,0)(1,1)(3,-1)(5,1)(7,-1)(9,1)(11,-1)(12,0)(14,0)
    \squigbijtriangle(-5,-2){#3}
    \squigbijtriangle(17,14){#3}
  \end{picture}%
  }}






% «chars»  (to ".chars")
% (find-LATEX "2019oxford-chars.tex")
% \ifluatex
%   \catcode`¹=13 \def¹{^{*}}
%   \catcode`²=13 \def²{^{**}}
%   \catcode`³=13 \def³{^{***}}
% \else
%   \DeclareUnicodeCharacter{00B9}{^{*}}              % ¹
%   \DeclareUnicodeCharacter{00B2}{^{**}}             % ²
%   \DeclareUnicodeCharacter{00B3}{^{***}}            % ³
% \fi




% Local Variables:
% coding: utf-8-unix
% ee-tla: "jod"
% End:
